Hyperbolic polynomial diffeomorphisms of \(\mathbb C^2\). II: Hubbard trees
type: Item
instance of: scholarly article
title: Hyperbolic polynomial diffeomorphisms of \(\mathbb C^2\). II: Hubbard trees
zbMATH Open document ID: 1168.37012
author: Yutaka Ishii
published in: Advances in Mathematics
publication date: 2009-02-25T00:00:00Z
review text: This paper is a continuation of Part I [\textit{Y. Ishii}, Adv. Math. 218, No. 2, 417--464 (2008; Zbl 1136.37028)]. The purpose of the current paper is to construct an object analogous to a Hubbard tree consisting of a pair of trees decorated with loops and a pair of maps between them for certain complex Hénon map or, more generally, a polynomial diffeomorphism \(f\) of \(\mathbb{C}^2\). The authors also show that a Hubbard tree gives a topological model for the dynamics of \(f\) on its Julia set in terms of its finite data. Recall that a Hubbard tree describes how the orbits of the critical points of a polynomial are sitting inside its Julia set.
reviewed by: Iuliana Oprea
Mathematics Subject Classification ID: 37F20
Mathematics Subject Classification ID: 37C50
Mathematics Subject Classification ID: 37E25
Mathematics Subject Classification ID: 37F15
zbMATH DE Number: 5518752
zbMATH Keywords: Hubbard trees
zbMATH Keywords: Hénon maps
zbMATH Keywords: Julia sets
zbMATH Keywords: hyperbolicity
zbMATH Keywords: branched manifolds
zbMATH Keywords: homotopy shadowing
MaRDI profile type: Publication
full work available at URL: j.aim.2008.09.015
OpenAlex ID: W2017151141
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DOI: 10.1016/J.AIM.2008.09.015
description: scientific article; zbMATH DE number 5518752